If the LCM of A and B is 72 and their HCF is 6, what is the

Question

If the LCM of A and B is 72 and their HCF is 6, what is the product of A & B?

Thanks guys!

OA: 432

Bunuel · Accepted Answer

The most important property of LCM (the least common multiple) and GCD (the greatest common divisors) is: for any positive integers x and y , x*y=GCD(x,y)*LCM(x,y) , so AB=72*6=432. Questions to practice: if-x-and-y-are-positive-integers-is-xy-a-multiple-of-102540.html if-x-and-y-are-positive-integers-what-is-the-value-of-xy-95872.html if-the-least-common-multiple-of-integers-x-and-y-is-105745.html#p827452 (Karishma's post explaining this property) Hope it helps.

vomhorizon · Answer

LCM of two numbers x GDF of the two numbers = Product of the two numbers ...

Therefore Product of A and B = 432 ...

Stiv · Answer

Example:
You have two numbers x=8 and y=12.
LCM of x,y = 24
GCF of x,y = 4

(LCM of x and y) X (GCF of x and y) = XY 
 24 X 4 = 8 X 12
 96 = 96

nk9285 · Answer

Product A*B= lcm*hcf(gcd)= 72*6= 423

Narenn · Answer

Try to understand why is so.

take two numbers a and b

The prime factorization of those numbers is

a= d,d,e,r
b=d,e,g,h,i

HCF of a and b = d,e
LCM of a and b = d,e,d,r,g,h,i
Product of HCF and LCM = d.e.d.e.d.r.g.h.i ---------> d^3.e^2.r.g.h.i
Product of Numbers = d.d.e.r.d.e.g.h.i --------------> d^3.e^2.r.g.h.i

in my opinion it is better to understand any theorem/rule than to remember it.

Hope it clears!

Regards,

Abhijit.

Godsent · Answer

The product of any two positive integers x and y is equivalent to the product of the square of their hcf and other individual numbers,or the product of their lcm and hcf.
X*Y=HCF^2 * P =LCM*HCF
where P is other individual numbers(i.e let's say X = 6:1*2*3 and Y =8:1*2*2*2, the hcf of X and Y is 2 and P is 1*3*1*2*2)
therefore X*Y =LCM*HCF= 72*6 =432

ConfusedSEA · Answer

I believe you refer to 432 instead of 423.

Abhishek009 · Answer

Must be so , if you consider the units digit 2*6 = Units digit 2

Victz · Answer

One way I visualize GCD*LCM=a*b is by thinking about the two numbers' prime box (set of prime factors):
e.g. 
70: 2 5 7
30: 2 3 5

GCD: pull out  mutual  factors: 2 5; multiply = 10 = GCD
LCM: pull out  all  factors and cross out duplicated ones: 2 5 7 X 3 X; multiply = 210 = LCM.
Notice the crossed-out factors in LCM are actually the ones in GCD. Thus, when you GCD * LCM, you reunite all factors, getting you back to a * b.

Hope it helps.

Basshead · Answer

The product of two numbers is equal to the product of its GCF and LCM.

72 * 6 = 432

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If the LCM of A and B is 72 and their HCF is 6, what is the

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If the LCM of A and B is 72 and their HCF is 6, what is the

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